Unveiling the evolving fracture toughness: The R-curve phenomenon in double network hydrogels

Double network (DN) hydrogels exhibit remarkable mechanical properties, most notably their high fracture toughness, which expands their potential applications across various fields. To guarantee the reliability of DN gels in practical uses, an in-depth comprehension of their fracture characteristics is crucial. Previous studies on the fracture behavior of DN gels mainly concentrated on the crack initiation process, often treating fracture toughness as a constant characteristic of the material. In contrast, our experimental research unveils the evolving fracture toughness as a fracture resistance curve (R-curve) in DN gels, indicating that fracture toughness increases with crack propagation until reaching a plateau of steady-state, rather than remaining constant. This phenomenon is attributed to mechanisms of crack tip softening and stress de-concentration resulting from the fracture of the brittle PAMPS network in DN gels. We have identified three critical parameters, i.e., the initiation fracture toughness (G_init), steady state toughness (G_ss), steady state crack extension length (L_ss), to quantify this behavior. Additionally, we explore the effect of pre-damage of PAMPS network on the R-curve and develop a theoretical model linking the degree of pre-damage (h) to G_ss. Our model effectively predicts the R-curve of DN gels under various pre-damage conditions. Furthermore, by considering different PAMPS network formulations, we establish a scaling law linking (G_ss−G_init) with L_ss, thus creating a unified framework for understanding the internal physical properties of diverse DN gels. These insights also differentiate the toughening mechanisms in DN gels: energy dissipation from the PAMPS network affects (G_ss−G_init), while the G_init reflects the intrinsic fracture properties governed by the elastic PAAm network. We anticipate that our experimental results and theoretical models will enhance the understanding of fracture in soft tough materials.